In this appeal from the denial of a petition for a writ of habeas corpus, petitioner James G. DiGiacomo claims that he was denied a fair trial when the state was allowed to use mathematical probability to identify him as the perpetrator of a crime. We hold that the admission of the challenged testimony violated no right guaranteed by the Constitution and affirm the district court's judgment denying the petition.

2

* In March 1977, James G. DiGiacomo was tried in an Illinois state court on charges of rape, deviate sexual assault, aggravated kidnapping, and battery. The principal witness against DiGiacomo was Patricia Marik, the victim of the assault. Marik testified that DiGiacomo abducted her at knife point from a tavern in Naperville, Illinois, on November 5, 1976, and ordered her to drive him to a cornfield in the country where, after a brief struggle, he forced her to have sexual intercourse with him.1

3

In an effort to bolster Marik's identification of DiGiacomo as her assailant at trial, the state called an expert witness to testify concerning a number of hairs that had been recovered from Marik's automobile after the attack. Sally Dillon, the supervising criminologist at the Illinois Bureau of Identification, testified that she had compared the hairs found in Marik's car with a sample of DiGiacomo's hair and found them to be microscopically similar. She was then asked, over defense counsel's objection, whether she could testify as to the statistical probability of the hair found in Marik's car belonging to someone other than DiGiacomo. Dillon responded that based on a recent study she had read, "the chances of another person belonging to that hair would be one in 4,500."

4

Several hours after beginning their deliberations, the jury, apparently confused by Dillon's testimony, submitted the following question to the court in writing: "Has it been established by sampling of hair specimens that the defendant was positively proven to have been in the automobile?" After consulting with the parties, the trial judge sent a written response to the jury in which he instructed them that it was their duty to determine the facts from the evidence presented at trial and that he could therefore provide no answer to their question. Neither side objected.

5

The jury later returned guilty verdicts on each of the charges, and DiGiacomo was sentenced to three concurrent terms of eight to twenty-five years for the kidnapping, rape, and deviate sexual assault, and 364 days, also concurrent, for the battery. DiGiacomo appealed his conviction to the Illinois Appellate Court, claiming, inter alia, that the trial court had erred in permitting the state to use mathematical odds to identify him as the perpetrator of a crime. The Appellate Court held that Dillon's testimony was properly admissible and affirmed the conviction. People v. DiGiacomo, 71 Ill.App.3d 56, 27 Ill.Dec. 232, 388 N.E.2d 1281 (2d Dist. 1979). Leave to appeal further was denied by the Illinois Supreme Court.

6

His state remedies thus exhausted, DiGiacomo filed a petition for habeas corpus in the United States District Court for the Northern District of Illinois in which he claimed that the admission of Dillon's testimony regarding the statistical likelihood of the hairs found in Marik's car belonging to him constituted a denial of due process. The district court denied the petition, and this appeal followed.

II

7

Under 28 U.S.C. § 2254, a federal court is authorized to issue a writ of habeas corpus in behalf of a person in custody under the judgment of a state court "only on the ground that he is in custody in violation of the Constitution or laws or treaties of the United States." Because the admissibility of evidence in state courts is a matter of state law, evidentiary questions are not subject to federal review under § 2254 unless there is a resultant denial of fundamental fairness or the denial of a specific constitutional right. United States ex rel. Clark v. Fike, 538 F.2d 750, 757 (7th Cir. 1976), cert. denied, 429 U.S. 1064, 97 S.Ct. 791, 50 L.Ed.2d 781 (1977).

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8

In this case, DiGiacomo contends the admission of expert testimony as to the mathematical likelihood of hairs found in Marik's car belonging to him resulted in a denial of fundamental fairness in that it misled the jury into believing that the state had conclusively established that he was in the car.2 In support of his contention, DiGiacomo cites the Eighth Circuit's decision in United States v. Massey, 594 F.2d 676 (8th Cir. 1979).

9

In Massey, the court held that the trial judge's comments construing expert testimony with respect to comparison of hair samples in terms of mathematical probability of error, coupled with the prosecutor's emphasis upon the mathematical probabilities in his closing argument, constituted plain error under Rule 52(b), Fed.R.Crim.P., and required reversal of the defendant's bank robbery conviction even though no objection had been made at trial. The expert in that case had testified that three of five hairs found in a blue ski mask similar to one worn by one of the perpetrators of the robbery were microscopically similar to the defendant's hair. He was then asked by the trial judge how many people in the country might have similar hair that could not be distinguished. The expert responded that in his own experience there had been only a "couple" cases out of over 2,000 in which he had been unable to distinguish hair from two different individuals. He added, however, that according to a recent study, apparently the same study on which Dillon had based her testimony, there was a one in 4,500 chance of another person having the same hair. 594 F.2d at 679. In an attempt to clarify the response, the trial judge asked the witness if this meant there was only a one in 4,500 or one in 2,000 chance of his identification being wrong. Although the expert's response was somewhat confusing, the prosecutor later emphasized these numbers throughout his closing argument to the jury, concluding with the statement that by itself "the hair sample would be proof beyond a reasonable doubt because it is so convincing." 594 F.2d at 681.

10

In reversing the conviction, the Eighth Circuit held that not only had the Government failed to establish a proper foundation for these mathematical conclusions, but in his closing argument the prosecutor had confused the identification of the hair found in the ski cap with the identification of the perpetrator of the crime. 594 F.2d 580, 581. Because of this confusion by the prosecutor and the potential for confusion already inherent in such evidence, the court concluded that plain error had been shown.

11

DiGiacomo contends that his case is even stronger because the record shows more than a mere possibility that the jury was confused. Here, he contends, it is apparent from the written question the jury submitted to the trial court shortly after beginning its deliberations that the jury was in fact confused by the expert testimony. The jury's confusion, which the trial judge's response wholly failed to remedy, he contends, clearly warrants the granting of federal habeas relief.

12

We agree that the interjection into the criminal trial process of sophisticated theories of mathematical probability raises a number of serious concerns.3 As one court has aptly stated, "(m)athematics, a veritable sorcerer in our computerized society, while assisting the trier of fact in the search for truth, must not cast a spell over him." People v. Collins, 68 Cal.2d 319, 320, 66 Cal.Rptr. 497, 438 P.2d 33, 36 A.L.R.3d 1176 (1968). While perhaps the most serious danger in admitting evidence of statistical probability in a criminal trial is the possibility that it will be used improperly, see People v. Collins, 68 Cal.2d 319, 66 Cal.Rptr. 497, 438 P.2d 33, 36 A.L.R.3d 1176, the possibility of prejudice also exists even when it is used in accordance with generally accepted principles. In a case involving the admissibility of virtually the same testimony with which we are faced here, the Supreme Court of Minnesota noted:

13

Testimony expressing opinions or conclusions in terms of statistical probabilities can make the uncertain seem all but proven, and suggest, by quantification, satisfaction of the requirement that guilt be established "beyond a reasonable doubt." See, Tribe, Trial by Mathematics, 84 Harv.L.Rev. 1329. Diligent cross-examination may in some cases minimize statistical manipulation and confine the scope of probability testimony. We are not convinced, however, that such rebuttal would dispel the psychological impact of the suggestion of mathematical precision, and we share the concern for "the substantial unfairness to a defendant which may result from ill conceived techniques with which the trier of fact is not technically equipped to cope." People v. Collins, 68 Cal.2d 332, 66 Cal.Rptr. 505, 438 P.2d 41.

14

State v. Carlson, 267 N.W.2d 170, 176 (Minn.1978) footnote omitted). Because of the danger that such evidence could mislead or confuse the jury, the court concluded in Carlson that an expert's testimony regarding the mathematical probability of certain incriminating hairs belonging to someone other than the defendant was improperly received. The court went on to hold, however, that under the facts of that case the error was harmless.

15

Even though we share in the concern of these courts that the admission of evidence as to mathematical probability in a criminal trial may mislead and confuse the jury, we do not find on the facts before us that its admission here constituted a denial of due process. Unlike Massey, the prosecutor in this case did not suggest in his closing argument that the mathematical odds testified to by the expert witness made her identification of the hair specimen virtually certain. In fact, the prosecutor conceded during argument that "some people have hair like that."4 Furthermore, the prosecutor in this case did not confuse the issue of whether the hairs found in the car were DiGiacomo's with the issue of whether he in fact committed the crime, although DiGiacomo concedes that in this case the questions are one and the same.

16

Although it may be true, as the question submitted to the trial court would seem to indicate, that one or more members of the jury were nevertheless confused about the significance of the hair identification testimony, we cannot say that this confusion was caused by any error of constitutional magnitude. Generally, the admission of expert testimony is very much a matter within the broad discretion of the trial judge. United States v. Tranowski, 659 F.2d 750, 755 (7th Cir. 1981). The Constitution does not and, indeed, cannot guarantee that only completely reliable evidence will be placed before the jury. Although it does demand that a defendant be given a full and fair opportunity to challenge whatever evidence is admitted, Chambers v. Mississippi, 410 U.S. 284, 298, 93 S.Ct. 1038, 1047, 35 L.Ed.2d 297 (1973), DiGiacomo was afforded that opportunity here. Through his counsel, he was free to challenge Dillon's testimony if it was not true, or clarify it if it was misleading. He was also free to call his own expert if he thought Dillon's testimony was at odds with the established views of the scientific community. DiGiacomo in fact did none of these things. No attempt was made to cross-examine Dillon regarding her testimony that the hairs found in Marik's car belonged to the defendant.

17

Even now, DiGiacomo does not claim that Dillon was wrong in her conclusion as to the likelihood of the hair found in Marik's car belonging to someone other than him. His contention is only that she should not have been allowed to express that conclusion in terms of mathematical probability. Instead, he contends she should have stated only whether or not the hairs were similar. But to limit her testimony in this way would have robbed the state of the full probative value of its evidence. To say that the defendant's hair is merely similar to hair found in the victim's automobile is significantly different than saying that there's a one in 4,500 chance of it belonging to someone else. If the expert's testimony is the latter, we know of no constitutional principle by which its admission could be held improper. While the better practice may be for the court specifically to instruct the jury on the limitations of mathematical probability whenever such evidence is admitted, we have no authority to impose such a rule upon the Illinois courts. Thus, we are unable to say that DiGiacomo's conviction resulted from a denial of any right guaranteed by the Constitution.

18

Of course, jury confusion by itself, even when not the product of a constitutional violation, could justify the granting of habeas relief if it resulted in a verdict that no rational trier of fact could have reached on the basis of the evidence presented. Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 2789, 61 L.Ed.2d 560 (1979). But DiGiacomo does not argue that no rational trier of fact could have found him guilty and, even if he did, the record does not support such a claim. Marik's positive identification of him as the man who had assaulted her together with the other evidence introduced by the state was more than sufficient to support a rational jury's verdict of guilty.

After preliminary examination of the briefs, the court notified the parties that it had tentatively concluded that oral argument would not be helpful to the court in this case. The notice provided that any party might file a "Statement as to Need of Oral Argument." See Rule 34(a), Fed.R.App.P. (effective Aug. 1, 1979); Circuit Rule 14(f). No such statement having been filed, the appeal has been submitted on the briefs and record

DiGiacomo was also identified by Kathryn Zrout, who earlier that same evening had been abducted at knife point from the same tavern and forced to drive to the same field where she also was sexually assaulted. Zrout's identification of DiGiacomo as the man who had attacked her was admitted under the Illinois evidentiary rule allowing proof of other crimes to show similar modus operandi. See People v. McDonald, 62 Ill.2d 448, 455, 343 N.E.2d 489, 492-93 (1976)

DiGiacomo does not claim that identification evidence based on microscopic analysis of hair samples is inadmissible by itself, but only that the conclusions reached from such analysis should not be expressed in terms of mathematical probability. In this respect, his claim differs from the claim asserted in United States v. Brown, 557 F.2d 541 (6th Cir. 1977). In that case, the Sixth Circuit held that microscopic analysis of hair specimens was inadmissible because it had not been shown to "carry sufficient indicia of reliability and accuracy to be said to cross 'the line between the experimental and demonstrable stages.' " 557 F.2d at 557, quoting Frye v. United States, 54 App.D.C. 46, 293 F. 1013, 1014 (1923). This court rejected a claim that expert testimony based on microscopic analysis of hair samples was not based on a reasonable scientific certainty in United States v. Cyphers, 553 F.2d 1064, 1071-72 (7th Cir. 1977)

For a fuller development of the advantages and disadvantages likely to flow from the use of statistical probability in the trial process, see Finkelstein and Fairley, A Bayesian Approach to Identification Evidence, 83 Harv.L.Rev. 489 (1970); Tribe, Trial by Mathematics: Precision and Ritual in the Legal Process, 84 Harv.L.Rev. 1329 (1971); Finkelstein and Fairley, A Comment on "Trial by Mathematics," 84 Harv.L.Rev. 1801 (1971); and Tribe, A Further Critique of Mathematical Proof, 84 Harv.L.Rev. 1810 (1971)

The prosecutor did not argue that the hair comparison proved anything by itself. He merely stated it was circumstantial evidence which, like other evidence in the case, tended to corroborate Marik's identification of DiGiacomo as the man who had attacked her. The only portion of his argument in which he referred to the hair identification evidence was as follows:

We have got circumstantial evidence, as well, and you are entitled to consider that circumstantial evidence.

It tends to prove the case. It is corroborative, certainly.

That is the circumstantial evidence of the defendant's hair found in that car.

It certainly isn't very likely, as you have heard, that any other person with hair like that was present in that car.

Likewise, you have the fact that the defendant was arrested the very next morning in that vicinity in Naperville.

It's a big world, but he just happens to be in Naperville.

Not only is he there, he has also got the jacket and he's wearing levis (sic).

Of course you will hear "Well, levis (sic), a lot of people wear levis (sic)."